A New Length-Biased Xrama Distribution: Properties and Application to Cancer Data

Authors

  • R. Jothika

    Research Scholar, Department of Statistics, Annamalai University, Chidambaram, Tamil Nadu-608002, India

  • P. Pandiyan

    Professor, Department of Statistics, Annamalai University, Chidambaram, Tamil Nadu-608002, India

Received date: June 11, 2025

Accepted date: July 16, 2025

Published date: July 20, 2025

DOI:

https://doi.org/10.14419/ytn4h313

Keywords:

Length-Biased Xrama Distribution; Statistical Properties; Reliability; Likelihood Ratio Tests

Abstract

This research introduces the Length-Biased Xrama distribution, an extension of the Xrama model. The study analyzes the length-biased ‎distribution's characteristics, comparing it to the original Xrama distribution, and investigates its statistical properties like moments and relia‎bility. Furthermore, the paper explores order statistics and likelihood ratio tests and utilizes Maximum Likelihood Estimation (MLE) to ‎determine the distribution's parameters. The findings, supported by real-world cancer data applications, suggest that the Length-Biased ‎Xrama distribution provides a superior fit compared to competing distributions‎.

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Received date: June 11, 2025

Accepted date: July 16, 2025

Published date: July 20, 2025